This is probably going to be laughed at, but when you sign-in try entering in your psn password manually, that is take it off auto sign-in, do the opposite if you enter it manually. I had this problem earlier this week, (after not playing UC3 since TLOU cam out) thought I'd have to change the DNS but this seemed to help.
Not for me. I foolishly waited almost an hour one time just waiting for it to try and sync (I was multi-tasking: I didn't want to stand around staring at the screen the whole time, especially for an hour, ugh). It didn't even move for most of that whole time, once agin it got stuck at the 'g' in 'syncing'. I'm starting to think it must be a patch problem, because I've experienced this same problem since last year, but then after I stopped playing for a few months, I had to update to a new patch and it worked again, hmm :/
Batman arkham city was more glitchy than bioshock infinite. Besides B:AC being older than BI, I still had more issues with it. However it's not the most glitchiest game I've ever played: that infamous title goes to AC3. But that's a whole different rant...I don't think my issues trying to play UC3 is a hardware issue (maybe it is? I don't know).
I was sick of waiting at the 'syncing level data' part so I was just bored and was comparing my trophiesto randomly selected people on my PSN list, when I saw that it got up to 'connecting'. I haven't played UC3 since April so when I of o main multiplayer home screen I immediately tried to invite one if my buddies. Then it got stuck on 'creating party', after I couple of minutes i gave up and quit the game which of course restarted my ps3. I tried again and got a buddy to invite me. It worked and I played two co-op games on crushing (which we didn't beat, since the random kept dying then left us).
I actually don't know what temporarily 'fixed' the issue but this is what I did today: 1. I vacuumed the ps3 vents 2. Deleted the 1.17 patch and reinstalled it 3. Changed the time via the Internet in settings 4. Deleted my info, unchecked 'save password' and manually re--entered my PSN info again
^ after all that, it still wouldn't sync and got stuck at the 'g' in 'syncing level data' as always. After waiting for almost 45 minutes I was literally 1 second away from logging out and turning off my ps3 when I was comparing trophies with people, then it wa connecting. I don't know how but it worked...for today at least.